Question

Answer.com after three half-lives, what fraction of a radioactive sample has decayed?

Answer 1

After 1 half-life, 1/2 the sample has decayed. After 2 half-lives 3/4 of the matter has decayed. So after, 3 half-lives about 11/12 would have decayed.

Answer 2

Answer: Thus the fraction decayed is
`(7a_o)/(8)`

Step-by-step explanation: Radioactive decay follow first order kinetics.

Now, to calculate the amount decayed after n half lives, we use the formula:

`a=(a_o)/(2^n)`

where,

a = amount of reactant left after n-half lives

`a_o` = Initial amount of the reactant

n = number of half lives = 3

Putting values in above equation, we get:

`a=(a_0)/(2^3)`

`a=(a_0)/(8)`

The fraction decayed after 3 half lives will be
`(1)/(8)` of the initial amount.

Thus the fraction decayed is
`a_0-(a_0)/(8)=(7a_o)/(8)`